In:
Mathematical Models and Methods in Applied Sciences, World Scientific Pub Co Pte Ltd, Vol. 28, No. 07 ( 2018-06-30), p. 1291-1336
Abstract:
We consider a model Poisson problem in [Formula: see text] ([Formula: see text] ) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ([Formula: see text]) or small faces ([Formula: see text] ). Our results extend the ones in [L. Beirão da Veiga, C. Lovadina and A. Russo, Stability analysis for the virtual element method, Math. Models Methods Appl. Sci. 27 (2017) 2557–2594] for the original two-dimensional virtual element method from [L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013) 199–214] to the version of the virtual element method in [B. Ahmad, A. Alsaedi, F. Brezzi, L. D. Marini and A. Russo, Equivalent projectors for virtual element methods, Comput. Math. Appl. 66 (2013) 376–391] that can also be applied to problems in three dimensions.
Type of Medium:
Online Resource
ISSN:
0218-2025
,
1793-6314
DOI:
10.1142/S0218202518500355
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2018
SSG:
11
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